All multi-tools are not created equal, but most with a plethora of features will get plenty of the jobs done. I personally like, and use often, the Lezyne RAP-21 LED tool, which will run you around $30. I like it because not only is it a high quality construction, but it has just about everything you’ll need, plus a sweet mini light. This will give you a chain breaker, spoke wrench, disc brake wedge, and all the most often used Allen keys and drivers. We’re talking a decent number of tools for 1/4 of what they would cost buying them separately.
Friction gear systems are a lot simpler to adjust, because the movement of the derailer cable can be modulated as you ride, every time you change the gear- they require less cycle maintenance. Modern index shifting systems are a little more complicated because each ‘click’ must release the exact right amount of cable to allow the derailer to move the correct distance to move the chain from one gear to another. Setting up and adjusting a derailer is not difficult and requires only basic tools, but there is a methodical procedure to follow.